Question: The heat flux along a cooling tube in a typical nuclear power reactor may often be approximated by

where L is the length of the tube and x is the distance along the tube. A particular air-cooled reactor is to be constructed of a stack of fuel plates with a 3 mm air space between them. The length of the flow passage will be 1.22 m, and the heat flux at the plate surfaces will vary according to the above equation with a = 900 W/m2 and b = 2500 W/m2. The air mass velocity is to be 7.5 kg/(s . m"). The air enters the reactor at 700 kPa and 100°C. Prepare a scale plot of heat flux, air mean temperature, and plate surface temperature as a function of distance along the flow passage. Although the heat flux is not constant along the passage, the passage length-to-gap ratio is sufficiently large that the constant-heat-rate heat transfer solution for the conductance h is not a bad approximation. Therefore, assume h is. a constant. We are most interested here in the peak surface temperature; and if this occurs in a region where the heat flux is varying only slowly, the approximation is still better. This is a point for discussion. The properties of air at 250°C may be used and treated as constant.